Six adaptive, short-term post-processing methods for correcting systematic errors in numerical weather prediction (NWP) forecasts of near-surface air temperatures using local meteorological observations are assessed and compared. The methods tested are based on the simple moving average and the more advanced Kalman filter. Forecasts from the rather coarse-resolution global NWP model Global Forecast System (GFS) and the regional high-resolution NWP model HARMONIE are post-processed, and the results are evaluated for 100 private weather stations in Denmark. The performance of the post-processing methods differs depending on the NWP model. Overall, the combined moving average and a so-called lead time Kalman filter performs the best. The moving average was shown to be superior to a diurnal bias correction Kalman filter at removing the longer-term systematic errors for HARMONIE forecast data and comparable for GFS forecast data. Subsequent application of the lead time Kalman filter corrects for the short-term errors using the real-time forecast error. The post-processing method is adaptive and there is no need for a long record of observations or a historical archive of forecasts.